C\ast-geometric phase for mixed states: entanglement, decoherence and spin system

TL;DR

This paper explores a new type of geometric phase in entangled mixed quantum states, revealing how it relates to decoherence, entanglement, and gauge structures, with implications for understanding quantum system evolution.

Contribution

It introduces a C extasterisk{}-geometric phase framework for entangled mixed states, linking geometric phases to gauge structures and decoherence effects in quantum systems.

Findings

Identifies two behaviors of geometric phases: one akin to Berry's phase and another related to decoherence.

Shows gauge structures resemble magnetic monopoles and instantons.

Analyzes the impact of geometric phases on the evolution of density matrix coherence.

Abstract

We study a kind of geometric phases for entangled quantum systems, and particularly a spin driven by a magnetic field and entangled with another spin. The new kind of geometric phase is based on an analogy between open quantum systems and dissipative quantum systems which uses a C\ast-module structure. We show that the system presents from the viewpoint of their geometric phases, two behaviours. The first one is identical to the behaviour of an isolated spin driven by a magnetic field, as the problem originally treated by Berry. The second one is specific to the decoherence process. The gauge structures induced by these geometric phases are then similar to a magnetic monopole gauge structure for the first case, and can be viewed as a kind of instanton gauge structure for the second case. We study the role of these geometric phases in the evolution of a mixed state, particularly by focusing on the evolution of the density matrix coherence. We investigate also the relation between the geometric phase of the mixed state of one of the entangled systems and the geometric phase of the bipartite system.